In a communication system, a technology to improve signal quality by performing digital signal processing on signals in a transceiver have been generally used. The technology to improve signal quality using the digital signal processing have already been put to practical use from the past in radio communication. Recently, in an optical communication field, a digital coherent communication system in which a digital signal processing circuit is installed in a transceiver has been studied.
The digital signal processing may compensates, for example, incompleteness of a device used for a communication apparatus or deterioration of a signal on a transmission line. For example, Japanese Laid-open Patent Publication No. 2012-120010 or Japanese Laid-open Patent Publication No. 2009-278613 discloses that an amplitude, a frequency, a polarization, or the like of signal is controlled by digital signal processing on a transmission side.
Here, one of compensation targets of the digital signal processing is non-linearity of characteristics of a transceiving device such as an amplifier (AMP), non-linear characteristics of a transmission line, or the like. The non-linearity of characteristics of the transceiving device is a compensation target common to the radio communication field and the optical communication field. In contrast, non-linear characteristics or wavelength dispersion characteristics of optical fibers used for an optical transmission line is a compensation target unique to the optical communication field.
One of technologies for pre-equalizing wavelength dispersion characteristics of optical fibers on a transmission side is disclosed in Japanese Laid-open Patent Publication No. 2008-211493. Meanwhile, one of technologies for compensating deterioration of signals caused by non-linear characteristics of an optical fiber is disclosed in Japanese Laid-open Patent Publication No. 2012-075097.
As one of methods for increasing communication capability, a technology for increasing a multivalued level in a modulation scheme is considered. However, as the multivalued level is increased, a higher signal-to-noise ratio (SNR) would be required. The SNR is improved by increasing power of a signal input to an optical fiber used for a transmission line. However, due to the non-linear characteristics of the optical fiber, as the power of an input signal increases, a signal would remarkably deteriorate due to non-linear distortion.
With respect to the above-described problem, Japanese Laid-open Patent Publication No. 2012-075097 discloses a technology for compensating non-linear distortion by using digital signal processing on a transmission side. According to Japanese Laid-open Patent Publication No. 2012-075097, propagation of a polarization multiplexed optical signal in an optical fiber is modeled by the Manakov equation as in Equation (A) below.
                                                                                          ∂                                                                                                          ∂                  z                                            ⁢                                                u                  H                                ⁡                                  (                                      t                    ,                    z                                    )                                                      +                                                            α                  ⁡                                      (                    z                    )                                                  2                            ⁢                                                u                  H                                ⁡                                  (                                      t                    ,                    z                                    )                                                      +                          j              ⁢                                                ⁢                                      (                    z                    )                                                  2                            ⁢                                                ∂                                                                                                          ∂                                      t                    2                                                              ⁢                                                u                  H                                ⁡                                  (                                      t                    ,                    z                                    )                                                              =                      j            ⁢                                                  ⁢                                          γ                ⁡                                  (                  z                  )                                            ⁡                              [                                                                                                                                                    u                          H                                                ⁡                                                  (                                                      t                            ,                            z                                                    )                                                                                                            2                                    +                                                                                                                                    u                          V                                                ⁡                                                  (                                                      t                            ,                            z                                                    )                                                                                                            2                                                  ]                                      ⁢                          u              H                        ⁢                                                  ⁢                          (                              t                ,                z                            )                                      ⁢                                  ⁢                                                                              ∂                                                                                                          ∂                  z                                            ⁢                                                u                  V                                ⁡                                  (                                      t                    ,                    z                                    )                                                      +                                                            α                  ⁡                                      (                    z                    )                                                  2                            ⁢                                                u                  V                                ⁡                                  (                                      t                    ,                    z                                    )                                                      +                          j              ⁢                                                ⁢                                      (                    z                    )                                                  2                            ⁢                                                ∂                                                                                                          ∂                                      t                    2                                                              ⁢                                                u                  V                                ⁡                                  (                                      t                    ,                    z                                    )                                                              =                      j            ⁢                                                  ⁢                                          γ                ⁡                                  (                  z                  )                                            ⁡                              [                                                                                                                                                    u                          V                                                ⁡                                                  (                                                      t                            ,                            z                                                    )                                                                                                            2                                    +                                                                                                                                    u                          H                                                ⁡                                                  (                                                      t                            ,                            z                                                    )                                                                                                            2                                                  ]                                      ⁢                          u              V                        ⁢                                                  ⁢                          (                              t                ,                z                            )                                                          (        A        )            
In Equation (A), uH(t, z) and uV(t, z) indicate electric field components of horizontal polarized and vertical polarized signals at a time t and a position z, respectively. Further, α(z), β2(z), and γ(z) indicate a damping coefficient, a dispersion coefficient, and a nonlinear coefficient of a fiber at the position z, respectively.
The non-linear distortion is obtained by solving a differential equation expressed in Equation (A) above. However, since it is complex to obtain a solution analytically, non-linear distortion obtained by using approximation is used for non-linear compensation.
In the technology disclosed in Japanese Laid-open Patent Publication No. 2012-075097, the Manakov equation expressed in Equation (A) is analyzed using the perturbation theory and the nonlinear distortion is compensated on the transmission side. That is, solutions uH(t=kT, z=L) and uV(t=kT, z=L) of nonlinear propagation of a horizontal polarized (H polarized) component and a vertical polarized (V polarized) component at a position L of a k-th symbol are expressed as in Equation (B) below and analyzed.uH(kT,L)=uH(kT,0)+ΔUH(k)uV(kT,L)=uV(kT,0)+ΔuV(k)   (B)
Here, uV(kT, 0)/uV(kT, 0) indicates an electric field at a position z=0 of the H/V polarized component and ΔuH(k)/ΔuV(k) indicates a perturbation term by a non-linear effect of the H/V polarized component.
When a signal of a k-th symbol of the H/V polarized component is considered to be a pulse with an amplitude AkH/V, Equation (C) below can be obtained.
                                                        u              H                        ⁡                          (                                                t                  =                  kT                                ,                                  z                  =                  L                                            )                                =                                                    u                H                            ⁡                              (                                                      t                    =                    kT                                    ,                  0                                )                                      +                                          ∑                                  m                  ,                  n                                                                                              ⁢                                                          ⁢                              {                                                      [                                                                                            A                                                      m                            +                            k                                                    H                                                ⁢                                                                              A                                                          n                              +                              k                                                        H                                                    ⁡                                                      (                                                          A                                                              m                                +                                n                                +                                k                                                            H                                                        )                                                                          ⁢                                            +                                                                        A                                                      m                            +                            k                                                    H                                                ⁢                                                                              A                                                          n                              +                              k                                                        V                                                    ⁡                                                      (                                                          A                                                              m                                +                                n                                +                                k                                                            V                                                        )                                                                          ⁢                                                              ]                                    ×                                      C                    ⁡                                          (                                              m                        ,                        n                        ,                                                  z                          =                          L                                                                    )                                                                      }                                                    ⁢                                  ⁢                                            u              V                        ⁡                          (                                                t                  =                  kT                                ,                                  z                  =                  L                                            )                                =                                                    u                V                            ⁡                              (                                                      t                    =                    kT                                    ,                  0                                )                                      +                                          ∑                                  m                  ,                  n                                                                                              ⁢                                                          ⁢                              {                                                      [                                                                                            A                                                      m                            +                            k                                                    V                                                ⁢                                                                              A                                                          n                              +                              k                                                        V                                                    ⁡                                                      (                                                          A                                                              m                                +                                n                                +                                k                                                            V                                                        )                                                                          ⁢                                            +                                                                        A                                                      m                            +                            k                                                    V                                                ⁢                                                                              A                                                          n                              +                              k                                                        H                                                    ⁡                                                      (                                                          A                                                              m                                +                                n                                +                                k                                                            H                                                        )                                                                          ⁢                                                              ]                                    ×                                      C                    ⁡                                          (                                              m                        ,                        n                        ,                                                  z                          =                          L                                                                    )                                                                      }                                                    ⁢                                  ⁢                  C          ⁡                      (                          m              ,              n              ,                              z                =                L                                      )                          ⁢                  ⁢                      ⁢                                                            γ                  ⁡                                      (                    z                    )                                                  ⁢                                  p                  ⁡                                      (                    z                    )                                                                                                1                  +                                      2                    ⁢                    j                    ⁢                                                                                  ⁢                                                                  s                        ⁡                                                  (                          z                          )                                                                    /                                              τ                        2                                                                              +                                      3                    ⁢                                                                  (                                                                              s                            ⁡                                                          (                              z                              )                                                                                /                                                      τ                            2                                                                          )                                            2                                                                                            ⁢            exp            ⁢                          {                                                -                                                            3                      ⁢                                                                                          ⁢                                              mnT                        2                                                                                                                                                                  τ                            2                                                    ⁡                                                      (                                                          1                              +                              3                                                        )                                                                          ⁢                        j                        ⁢                                                                                                  ⁢                                                                              s                            ⁡                                                          (                              z                              )                                                                                /                                                      τ                            2                                                                                              )                                                                      -                                                                                                    (                                                  m                          -                          n                                                )                                            2                                        ⁢                                          T                      2                                                                                                  τ                      2                                        ⁡                                          [                                              1                        +                                                  2                          ⁢                                                                                                          ⁢                          j                          ⁢                                                                                                          ⁢                                                                                    s                              ⁡                                                              (                                z                                )                                                                                      /                                                          τ                              2                                                                                                      +                                                  3                          ⁢                                                                                    (                                                                                                s                                  ⁡                                                                      (                                    z                                    )                                                                                                  /                                                                  τ                                  2                                                                                            )                                                        2                                                                                              ]                                                                                  }                        ⁢                          ⅆ              z                                                          (        C        )            
Here, m and n are integers. Further, p(z) indicates a signal power at the position z, s(z) indicates a total accumulated dispersion value in a transmission line for the purpose of propagation at the position z, τ indicates a half width of a pulse, and T indicates a pulse period. As understood from Equation (C) above, the perturbation term by the non-linear effect of the H/V polarized component indicates a sum of products of three amplitudes AkH/V. Further, C(m, n, z=L) is coefficient indicating the degree that a product of amplitudes in a combination of given n and m becomes non-linear distortion and is obtained by perturbation analysis.
In a signal processing circuit, as a to-be-processed signal becomes complex, bit accuracy is required to be higher, so that the size of the signal processing circuit becomes very large. Since a signal processed by the signal processing circuit of a reception side contains noise or distortion occurred in a transmission line or a transceiving device, the signal is processed as a multi-bit digital signal. Therefore, calculation of non-linear distortion becomes complex.